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If the magnitude of two vectors is 4 and 5 and the value of their scalar product is 10, then the angle between vectors is:

The maximum value of the term independent of $t$ in the expansion of ${(t{x}^{1/5}+\frac{(1-x{)}^{1/10}}{t})}^{10}$ where $x\in (0,1)$ is :

If $\alpha =3{\sin }^{-1}(\frac{6}{11})$ and $\beta =3{\cos }^{-1}(\frac{4}{9}),$ where the inverse trignometric functions takes only the principal values, then the correct option(s) is(are)

If $I_1={\int }_e^{e^2}\frac{dx}{logx}$ and $I_2={\int }_1^2\frac{e^x}{x}dx,$ then

If the arithmetic mean of the number $x_1,x_2,x_3.........,x_n$ is $\overline{x}$ , then the arithmetic mean of numbers$a{x}_1,+b,a{x}_2+b,a{x}_3+b,.............a{x}_n+b,$

where a, b are two constants would be

If $\alpha ,\beta$ are the roots of the equation $3x^2+5x-7=0$, then the equation whose roots are $\frac{1}{3\alpha +5},\frac{1}{3\beta +5}$ is

If the power of point $(2,1)$ with respect to the circle $2x^2+2y^2-8x-6y+k=0$ is positive, then

In how many ways can one select a cricket team of eleven from 17 players in which only 5 persons can bowl if each cricket team of 11 must include exactly 4 bowlers ?

The number of solutions for the equation $2si{n}^{-1}\sqrt{x^2-x+1}+co{s}^{-1}\sqrt{x^2-x}=\frac{3\pi }{2}$ is

For the given differential equation find the particular solution satisfying the given conditions.

$\frac{dy}{dx}-\frac{y}{x}+cosec\left(\frac{y}{x}\right)=0,y=0whenx=1.$

f(x) = 2+3cosx

Find the range

In an examination, out of $100$ students, $75$ passed in English, $60$ passed in Mathematics and $45$ passed in both English and Mathematics. The number of students who passed in none of the two subjects, is (Assume all students gave both the exams)

If the abscissa and ordinates of two points $P$ and $Q$ are the roots of the equations $x^2+2ax-b^2=0$ and $x^2+2px-q^2=0$ respectively, then the equation of the circle with $PQ$ as diameter is

The range of $f\left(x\right)=\frac{x+2}{x-3}$ is

The area (in square units) of the region bounded by the curves $y+2x^2=0\text{and}y+3x^2=1$, is equal to :

The minimum value of $27\sec x+64\text{cosec}x$ for $x\in (0,\pi /2)$ is

Let C be the set of complex numbers. Prove that the mapping $f:C\to R$ given by $f\left(z\right)=|z|,\forall z\in C$, is neither one-one nor onto.

The radian measure of $-{37}^{\circ }{30}^{\prime }$ is

Value of $S_1^2+S_2^2+...+S_n^2$ is

The area inside the parabola $5x^2–y=0$ but outside the parabola $2x^2–y+9=0$, is

Match $\text{List I}$ with the $\text{List II}$ and select the correct answer using the code given below the lists :



$\begin{array}{cccc}& \text{List - I}& & \text{List - II}\\ & \text{There are two boxes. In the first box, there are}2\text{white and}1\text{black balls, where in the second box, there is}1\text{white and}& & \\ \text{(A)}& 5\text{black balls. A ball is drawn from the first box and kept in the second and a ball drawn from the second box was found}& \text{(P)}& \frac{1}{8}\\ & \text{to be white. The chance that a black ball was transferred from first to the second box is}& & \\ \text{(B)}& 3\text{identical unfair coins are flipped. The probability that there are two heads and one tail is}\frac{2}{9}.\text{The probability that}& \text{(Q)}& \frac{1}{4}\\ & \text{there are two tails and one head is}\frac{4}{9}.\text{The probability that the coin will flip head, is}& & \\ \text{(C)}& \text{There are}n\text{distinct points on a circle. If two of these points are joined to form a line and then another two points}& \text{(R)}& \frac{1}{3}\\ & \text{(different from the first two) are joined to form another line, the probability that these two lines intersect inside the circle, is}& & \\ \text{(D)}& \text{If three fair dice are thrown, and the sum is an odd number, the probability that all three dice show an odd number is}& \text{(S)}& \frac{1}{5}\\ & & \text{(T)}& \frac{4}{7}\end{array}$



Which of the following is a CORRECT combination?

Let $f\left(x\right)=\{\begin{array}{cc}\left[x\right];& -2\le x\le -\frac{1}{2}\\ 2x^2-1;& -\frac{1}{2}<x\le 2\end{array}$ and $g\left(x\right)=f\left(|x|\right)+|f\left(x\right)|$, where $[.]$ represents the greatest integer function. The number of points where $g\left(x\right)$ is non-differentiable is

A variable plane which remains at a constant distance 3p from the origin cuts the co-ordinate axes at A, B, C. The locus of the centroid of triangle ABC is

If ${\sin }^{-1}\frac{3}{5}+{\cos }^{-1}\frac{12}{13}={\sin }^{-1}C,$ then $C=$

ABCD is a rectangle with vertex A(0,0) as shown in below figure where P and Q are midpoints of sides CD and BC respectively. If C =(8,6) then find the coordinates of P and Q.

The complete solution of the in equation $x^2-4x<12$ is